ECCOMAS 2024

Competition between stall cells and low-frequency global modes in transitional flows around airfoils near stall

  • Sarras, Konstantinos (ONERA)
  • Marquet, Olivier (ONERA)

Please login to view abstract download link

Turbulent flows around airfoils near stalling conditions may be characterized by low- frequency oscillations during which the flow alternates between attached and detached states, and by stall cells, that are spanwise modulation of the flow on the suction side of the airfoil. Recent studies [1, 2] have shown that the onset of these two phenomena can be captured using global stability analysis of the fully turbulent mean-flow estimated within the framework of the Reynolds-Averaged Navier Stokes (RANS) equations. In this talk, we will investigate the competition between these two global instabilities but for a transitional flow over a NACA 0012 airfoil at the Reynolds number Re = 90000. The transitional nature of the flow is modelled using the linear eddy-viscosity model developed by Spalart & Allmaras that is coupled here with a correlation-based algebraic transition model. Similarly to the fully turbulent cases mentionned before, the branch of steady solutions exhibits a S shape curve with two saddle-node bifurcations. The solutions of the high-lift branch are however characterized by the existence of a laminar separation bubble (LSB) at the leading edge. The global stability analysis of these steady solutions is based on the full linearization of the governing discrete equations, including the turbulence model, the transition model and the numerical stabilization terms. It reveals the existence of two unstable modes: a two-dimensional low-frequency mode similar to that found by [2] and a three-dimensional zero-frequency mode similar to that found by [1]. The competition between these two modes is investigated by following the corresponding eigenvalues along the branch of steady solutions. Thus, we have identified the critical angles for each mode and shown that the three-dimensional modes become unstable prior to the two-dimensional ones, for that particular case